Zhu et al. [1]} recently proposed a method that tries to learn the domain transform. Their method first processes the undersampled input data in k-space, learns the inverse discrete Fourier transform (iDFT), and then refines the result in the image domain. In the case of CS reconstruction, the domain transform can be considered as learning an approximation for the iDFT for undersampled k-space data. The domain transform is modeled as a sequence of connected layers, and the image domain refinement is modeled as a series of convolutional layers. A disadvantage of this approach is that the domain transform has a quadratic complexity with respect to the size of the input image. For example, when dealing with \(256\times 256\)  images, the number of learned parameters in their model would be greater \(>10^{10}\) . The quadratic order of the algorithm makes it challenging to use their model for typical MR image sizes due to current hardware limitations.
